## Coinductive counting: bisimulation in enumerative combinatorics (Extended Abstract) (2002)

Venue: | L. MOSS (ED.), THE PROC. CMCS’02, ENTCS, VOL. 65, ELSEVIER SCIENCE B.V |

Citations: | 1 - 1 self |

### BibTeX

@INPROCEEDINGS{Rutten02coinductivecounting:,

author = {J. J. M. M. Rutten},

title = {Coinductive counting: bisimulation in enumerative combinatorics (Extended Abstract) },

booktitle = {L. MOSS (ED.), THE PROC. CMCS’02, ENTCS, VOL. 65, ELSEVIER SCIENCE B.V},

year = {2002},

publisher = {}

}

### OpenURL

### Abstract

### Citations

183 |
Combinatorial Species and Tree-Like Structures, volume 67 of Encyclopedia of Mathematics and its Applications
- Bergereon, Labelle, et al.
- 1998
(Show Context)
Citation Context ...to an alternative approach to counting, which is based on structural properties expressed as a kind of domain equation (such asT =1+T X T for binary trees), as present in for instance [FS93] and also =-=[BLL98]-=-. (ii) The issue of minimization of weighted automata has of course only been touched upon. In the presented examples, there usually was an obvious minimized candidate, but a more systematic and algor... |

171 |
Rational Series and Their Languages
- Berstel, Reutenauer
- 1988
(Show Context)
Citation Context ... most of what we know aboutenumerative combinatorics: [GKP94], [FS93, FS01], and [Sta97, Sta99]. The use of continued fractions has been inspired by [Fla80]. A basic reference on weighted automata is =-=[BR88]-=-. 2 Basic facts from stream calculus We brie y summarize those parts of [Rut01] that are needed in the present paper. The set of all streams is de ned by IR ! = f j : f0; 1; 2;:::g!IR g. Individual st... |

146 | Combinatorial aspects of continued fractions
- Flajolet
- 1980
(Show Context)
Citation Context ... of the following texts, from which we have learned most of what we know aboutenumerative combinatorics: [GKP94], [FS93, FS01], and [Sta97, Sta99]. The use of continued fractions has been inspired by =-=[Fla80]-=-. A basic reference on weighted automata is [BR88]. 2 Basic facts from stream calculus We brie y summarize those parts of [Rut01] that are needed in the present paper. The set of all streams is de ned... |

29 |
Analitic combinatorics: functional equations, rational and algebraic functions
- Flajolet, Sedgewick
(Show Context)
Citation Context ...is worthwhile to develop also the multivariate case in some detail. (iv) In one case (Section 6), we have distinguished between rational and algebraic streams. Notably in the work of Flajolet, such as=-=[FS01]-=-,much more has already been said about the classi cation of streams (there rather: generating functions) in analytical terms. Looking at the various weighted automata that we have encountered sofar, w... |

23 |
Concrete mathematics, second edition
- Graham, Knuth, et al.
- 1994
(Show Context)
Citation Context ...he Transfer-matrix method, and many more. About all our example counting problems stem from one of the following texts, from which we have learned most of what we know aboutenumerative combinatorics: =-=[GKP94]-=-, [FS93, FS01], and [Sta97, Sta99]. The use of continued fractions has been inspired by [Fla80]. A basic reference on weighted automata is [BR88]. 2 Basic facts from stream calculus We brie y summariz... |

20 |
Elements of stream calculus (an extensive exercise in coinduction
- Rutten
(Show Context)
Citation Context ... queens at level k. Thus we have translated the original counting problem into a question about streams and their representation by automata, thereby entering the coinductive world of stream calculus =-=[Rut01]-=-. A crucial ingredient of stream calculus is the notion of stream bisimulation, with the help of which the above automaton can be simpli ed by identifying all equivalent states as follows. Every drone... |

17 |
The average case analysis of algorithms: Counting and generating functions
- Flajolet, Sedgewick
(Show Context)
Citation Context ...closely related to an alternative approach to counting, which is based on structural properties expressed as a kind of domain equation (such asT =1+T X T for binary trees), as present in for instance =-=[FS93]-=- and also [BLL98]. (ii) The issue of minimization of weighted automata has of course only been touched upon. In the presented examples, there usually was an obvious minimized candidate, but a more sys... |

1 | Enumerative Combinatorics I,volume 49 of Cambridge - Stanley - 1997 |

1 | Enumerative Combinatorics II, volume 62 of Cambridge - Stanley - 1999 |